History of Measurement

VFMS 2014

Mrs. Long

Measurement Notes

I. Historical units of measurement Length

1. Cubit = distance from the tip of the elbow to the tip of the middle finger.

2. Fathom = distance across a man’s outstretched arms. 3. Span – distance from pinky to thumb on an outstretched hand. 4. Digit – length of one finger.

Measurement Notes

Weight Babylonians improved upon the invention of

the balance by establishing the world’s first weight standards – polished stones!

Egyptians & Greeks used a wheat seed as the smallest unit of weight.

II. Timeline of measurement

Thirteenth century – King Edward of England, realized the importance of standardization – ordered the “iron ulna”.

1793 – Napoleon’s rule of France, the metric system was born! Based on the meter – supposed to be one-ten–millionth (1/10,000,000 ) of the Earth’s circumference (measured at 40,000 km)

II. Timeline of measurement

1960 – Officially adopted Systeme International (SI System) need for universal language in sciences recognized. Decimal system is based on units of 10.

Today – Accepted & used worldwide by scientist

III. Fundamental Units of Measurement

Quantity Unit Symbol

Length meter m

Mass gram g

Volume liter l

Time second s

Force newton N

Energy joule J

Metric System

The metric system is based on a base unit that corresponds to a certain kind of measurement

Length = meter Volume = liter Weight (Mass) = gram

Prefixes plus base units make up the metric system – Example:

Centi + meter = Centimeter Kilo + liter = Kiloliter

IV. Using the Metric SystemTo convert to a larger unit,

move the decimal point to the left or divide.

To convert to a larger unit, move the decimal point to the left or divide.

To convert to a smaller unit, move the decimal point to the right or multiply.

To convert to a smaller unit, move the decimal point to the right or multiply.

KING HENRY DECKED

BULLIES DRINKING

CHOCOLATE

MILK

Kilo Hecto

Deka Base Unit deci centi milli

K H D Volume: liter (l)Distance: Meter

(m)Mass: gram (g)

d c m

1000.0

100.0 10.0 1.0 0.1 0.01 0.001

BiggerBigger SmallerSmaller

Metric System

The three prefixes that we will use the most are:– kilo– centi– milli

Giga G

MEGAM

KILOk

HECTOh

DECAD

Base Units

metergramliter

decid

centic

millim

micro

nanon

LARGER than base unit smaller than base unit

Metric System

These prefixes are based on powers of 10. What does this mean?– From each prefix every “step” is either:

10 times larger or

10 times smaller– For example

Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters

GIGAG

MEGAM

KILOk

HECTOh

DECAda

Base Units

metergramliter

decid

centic

millim

micro

nanon

Metric System

If you move to the left in the diagram, move the decimal to the left

If you move to the right in the diagram, move the decimal to the right

kilo hecto deca

meterliter

gramdeci centi milli

Example #1

13.2 mg = ? g

Step 1: Identify that mg < g

Step 2: slide decimal point to the left 3 times13.2 mg

Step 3: put a “0” in front of the decimal and add correct unit to the number

0.0132 g

Example 2

5.7 km = ? cm

Step 1: Identify that km > cm

Step 2: slide decimal point to the right 5 times because kilometers are 5 units larger than centimeters

5.7 km

Step 3: put four “0’s” in behind the 7 and add the correct unit to the number

570,000 cm

Metric System Now let’s start from meters and convert to centimeters

5 meters = _____ centimeters

kilo hecto deca

meterliter

gramdeci centi milli

kilo hecto deca

meterliter

gramdeci centi milli

• Now let’s start from kilometers and convert to meters

.3 kilometers = _____ meters

500

300

Metric System

Review– What are the base units for length, volume and mass in

the metric system?– What prefix means 1000? 1/10?, 1/1000?– How many millimeters are in 12.5 Hm?– How many Kiloliters are in 4.34cl?

kilo hecto deca

meterliter

gramdeci centi milli

Metric System Now let’s start from meters and convert to kilometers

4000 meters = _____ kilometers

kilo hecto deca

meterliter

gramdeci centi milli

kilo hecto deca

meterliter

gramdeci centi milli

• Now let’s start from centimeters and convert to meters

4000 centimeters = _____ meters

4

40

V. Accuracy vs. Precision

1. Accuracy – nearness of a measurement to the standard or true value.

2. Precision – the degree to which several measurements provide answers very close to each other.

3. Percent error: a measure of the % difference between a

measured value and the accepted “correct” value formula: | correct – measured | x 100

= % error correct

VI. Significant Figures- Certain vs. Uncertain Digits:

Certain – DIGITS THAT ARE DETERMINED USING A MARK ON AN INSTRUMENT OR ARE GIVEN BY AN ELECTRONIC INSTRUMENT

Uncertain – THE DIGIT THAT IS ESTIMATED WHEN USING AN INSTRUMENT WITH MARKS (ALWAYS A ZERO OR FIVE – FOR THIS CLASS)

Significant figures

Rules Numbers other than zero are always significant 96 ( 2 ) 61.4 ( 3 ) One or more zeros used after the decimal point is

considered significant. 4.7000 ( 5 ) 32 ( 2 ) Zeros between numbers other than zero are always

significant. 5.029 ( 4 ) 450.089 ( 6 )

Zeros used at the end or beginning are not significant. The zeros are place holders only.

75,000 ( 2 ) 0.00651 ( 3 ) Rule for rounding-If the number to the right of the

last significant digit is 5 or more round up. If less than 5, do not round up.

Need 2 sig figs. For this value 3420 (3400 ) Need 3 sig figs. For this value 0.07876 ( 0.0788)

Significant Figures

Digits in a measured number that include all certain digits and a final digit with some uncertainty

Number Number of Sig Figs

9.120.192

0.0009129.00

9.120090.0900.900

3333533?

Addition and Subtraction- answer may contain only as many decimals as the least accurate value used to find the answer.

 

33.014+ 0.01 = 33.02   Multiplication and Division- answer may contain only as many sig. Figs. As the

smallest value used.

3.1670 x 4.0 = 12.668 13

Example State the number of significant figures in the following set of measurements:

a. 30.0 g b. 29.9801g c. 0.03 kg d. 31,000 mg e. 3102. cg

VII. Scientific Notation Scientific notation

Representation of a number in the form A x 10n

Scientists work with very large and very small numbers. In order to make numbers easier to work with, scientists use scientific notation.

Scientific notation- there must always be only one non-zero digit in front of the decimal.

In scientific notation, the number is separated into two parts. The first part is a number between 1 and 9. The second is a power of ten written in exponential form.

Examples: 100= 10x10= 102

1000= 10x10x10=103

0.1=1/10=10-1

.01=1/100=1/10x1/10=10-2

Converting numbers to Scientific notation

To write numbers in scientific notation, the proper exponent can be found by counting how many times the decimal point must be moved to bring it to its final position so that there is only one digit to the left of the decimal point (the number is between 1 and 9).

A(+) positive exponent shows that the decimal was moved to the left. It is moved to the right when writing the number without an exponent.

A (-) negative exponent shows that the decimal was moved to the right. It is moved to the left to get the original number.

Another method of deciding if the exponent is positive or negative is to remember that values less than one (decimals) will have negative exponents and values of one or greater than one have positive exponents.

Examples: 920=9.2x100=9.2x102

1,540,000=1.54x1,000,000=1.54x106

83500=8.35x10,000=8.35x104

0.018=1.8x.01=1.8x10-2

Scientific Notation

Representation of a number in the form A x 10n

Number Scientific Notation 0.000319 3,190,000

0.000000597

3.19x10-4 3.19x106 5.97x10-7

Scientific Notation Computation Rules:

Addition and Subtraction:

1.make the exponents match

2.add or subtract the coefficients

3.keep the exponent the same for the answer

4.correct the S.N. if it is not in the correct format

2x103+3x103 =

1.5x103 + 2.6x104 =

Scientific Notation Computation Rules:

Multiplication and Division:

1. multiply or divide the coefficients

2. add the exponents (for multiplication) or subtract the exponents (for division)

3. correct the S.N. if it is not in correct format

1x102 1.7x103 7.3x10-4/ 4.2x102 =

X 1.2x105 X 2.3x10-1

Tools of Measurement

Measuring Length Ruler Using the METRIC side Record all certain digits PLUS one uncertain

(record to the hundredths place) Units: cm, mm, m, km

Measuring Mass

Triple beam balance Uses three (sometimes 4) beams to measure the

mass of an object Place solid object directly on pan Place powders on filter paper or liquids in a

container; deduct mass of the paper or container from the final measurement

Start with riders at largest mass and work back until the pointer reaches zero

Record all certain (up to hundredths) plus one uncertain (thousandths)

Measuring Volume

Solids - Ruler Volume = length x width x height Units: cubic centimeter = cm3

Liquids – Graduated Cylinder Read the volume at the bottom of the meniscus Be sure to place the graduated cylinder on a flat surface and

look straight at the meniscus Caution: Be sure to determine the increments on the graduated

cylinder Record all certain (usually tenths) plus one uncertain (usually

hundredths) Units: generally ml

Unusually Shaped Objects – Water Displacement Determine the volume of a filled graduated cylinder Place the object in the graduated cylinder Determine the volume of the graduated cylinder with

the object Subtract the volume to determine the amount of

water displaced the volume of the solid

Measuring Temperature

Thermometer Read the level of alcohol in the tube to

determine the temperature Caution: When reading negative

temperatures be sure that you are reading in the correct direction

Units: degrees CelsiusTemperature (C)

30 is hot20 is nice

10 is chilly0 is ice

25 (F) 25 (C)

The Metric System: Conversions(APPROXIMATE)

Metric English 1 kilogram 1 kilometer

1 meter 1 centimeter

1 liter 1 liter

2.2 pounds 0.62 miles 1.09 yards 0.39 inches 1.06 quarts 0.26 gallons